Volume Of Fraction Method Research Articles

Experimental and numerical study on the temporal and spatial nonlinearity evolution of focused wave

Extreme waves pose a significant threat to coastal structures. Focused wave, representing the average shape of extreme waves, is frequently employed to simulate extreme waves. Despite its convenience of generating large amplitude waves, the nonlinearity evolution of focused wave during propagation has been seldom explored. It is obvious that the nonlinearity would influence the wave shape and energy structure during focusing. This study investigates the temporal and spatial nonlinearity evolution experimentally and numerically. The experiment was conducted in a wave tank using a piston-type wavemaker. The numerical model was set up with geometry adopted from physical experiment in the commercial software FLUENT. The turbulence model RNG k–ε was employed, while the volume of fraction method was used to capture the air-water interface. The high-order harmonics were extracted from the recorded wave elevations by the four-phase decomposing method. The evolution of high-order harmonics and the energy structure were obtained. It is validated that the high-order harmonics can be reasonably estimated by multiplying linear harmonics by harmonic coefficients calculated by Stokes III or V wave theory. This paper enhances the understanding of temporal and spatial nonlinearity evolution of focused wave, which would be helpful for structure design and site selection.

Film investigation of swirl-vane separator based on Euler grid approximation and coupled film method of Eulerian wall film and volume of fraction method

The movement of multiple liquid droplets within steam flow constitutes a commonplace and noteworthy phenomenon across a spectrum of disciplines, including environmental science, chemical engineering, and energy studies. To simulate the dynamic behavior of these droplets, the methodology of Euler grid approximation, along with the Eulerian wall film (EWF) coupled with the volume-of-fluid (VOF) method, was successfully employed to simulate the steam-liquid separation and liquid film processes within the swirl-vane separator. The trajectory of droplets within the gas phase field was constructed using the Euler grid approximation methodology, while the flow of liquid film formed by droplet–wall collision was modeled based on the coupled EWF and VOF liquid film model. The investigation of two-phase flow and liquid film flow within the swirl-vane separator under high temperature and pressure conditions was conducted utilizing the proposed model, with subsequent analysis of the pertinent characteristics of droplets and liquid film. Specifically, the thickness and velocity of the liquid film significantly increased with the increase in droplet mass flow rate, with larger droplets more prone to concentrate and form stable flow of thick liquid film. The study results may hold significant implications for the design, operation, and optimization of separators.

On ventilated supercavities moving horizontally near free surface

By means of open source CFD tool OpenFOAM platform, a multiphase solver capable to deal with two phases flows is used to investigate ventilated supercavities. The VOF (volume of fraction) method is employed in order to capture cavity interface and the free surface. The main objective of this work is to investigate ventilated supercavity generated after a disk-cavitator which moves horizontally near a free surface. Most of the work in this research has been focused on the shape of supercavity and its asymmetry. Furthermore, two distinct cavity closure types, i.e. the re-entrant jet (RJ) and the twin vortex (TV) and are discussed separately to compare their gas leakage mechanisms at different submergence ratio. Numerical results indicate that the air-water free surface will have a significant influence on the cavity surface curvature and gas shedding process. Under the influence of free surface, the length diameter ratio of ventilated cavitation increases with H‾ decrease with decrease. The influence of free boundary on the upper surface of cavitation interface is greater than that on the lower surface. When Fr number and ventilation volume are constant, when approaching the free surface, the interface curvature of ventilation cavitation will increase. The deflection of cavitation axis is mainly affected by gravity and free surface. When the Fr number is small, the cavitation axis will be slightly disturbed. When the Fr number is large, the cavitation axis deflects reversely. These may give meaningful references for the design of surface vehicles.

Numerical Investigation on the Flow Instability of Dispersed Bubbly Flow in a Horizontal Contraction Section

Dispersed bubbly flow is important to understand when working in a wide variety of hydrodynamic engineering areas; the main objective of this work is to numerically study bubble-induced instability. Surface tension and bubble-induced turbulence effects are considered with the momentum and k-ω transport equations. Steady dispersed bubbly flow is generated at the inlet surface using time-step and user-defined functions. In order to track the interface between the liquid and gas phases, the volume of fraction method is used. Several calculation conditions are considered in order to determine the effects of bubble diameter, bubble distribution, bubble velocity and bubble density on flow instability and void fraction. The void fraction of the domain is set to no more than 0.5% under different bubbly (micro/small) flow conditions; and the order of magnitude of the Reynolds number is 106. Results from the simulation indicate that velocity fluctuation induced by bubble swarm increases with increasing bubble diameter. Bubble density and bubble distribution seem to have a complex influence on flow instability. Bubble-induced turbulence results indicate that small bubbles produce a significant disturbance near the boundary region of bubble swarm; this indicates that induced bubble swarm has a potential capability of enhancing heat and mass transfer in the velocity boundary layer. Results from this study are useful for two-phase flow, bubble floatation and other hydrodynamic engineering applications.

CFD simulation of heat transfer and phase change characteristics of the cryogenic liquid hydrogen tank under microgravity conditions

The heat transfer and phase change processes of cryogenic liquid hydrogen (LH2) in the tank have an important influence on the working performance of the liquid hydrogen-liquid oxygen storage and supply system of rockets and spacecrafts. In this study, we use the RANS method coupled with Lee model and VOF (volume of fraction) method to solve Navier-stokes equations. The Lee model is adopted to describe the phase change process of liquid hydrogen, and the VOF method is utilized to calculate free surface by solving the advection equation of volume fraction. The model is used to simulate the heat transfer and phase change processes of the cryogenic liquid hydrogen in the storage tank with the different gravitational accelerations, initial temperature, and liquid fill ratios of liquid hydrogen. Numerical results indicate greater gravitational acceleration enhances buoyancy and convection, enhancing convective heat transfer and evaporation processes in the tank. When the acceleration of gravity increases from 10−2 g0 to 10−5 g0, gaseous hydrogen mass increases from 0.0157 kg to 0.0244 kg at 200s. With the increase of initial liquid hydrogen temperature, the heat required to raise the liquid hydrogen to saturation temperature decreases and causes more liquid hydrogen to evaporate and cools the gas hydrogen temperature. More cryogenic liquid hydrogen (i.e., larger the fill ratio) makes the average fluid temperature in the tank lower. A 12.5% reduction in the fill ratio resulted in a decrease in fluid temperature from 20.35 K to 20.15 K (a reduction of about 0.1%, at 200s).

Influence of Nozzle Orifice Shape on the Atomization Process of Si3N4 in a Dry Granulation Process

In order to reveal the intrinsic fluid-dynamic mechanisms of a pressure-swirl nozzle used for Si3N4 dry granulation, and effectively predict its external spray characteristics, the dynamics of air-atomized liquid two-phase flow is analyzed using a VOF (Volume of Fraction) method together with the modified realizable k-ε turbulence model. The influence of nozzle orifice shape on velocity distribution, pressure distribution is studied. The results show that the pressure difference in a convergent conical nozzle is the largest with a hollow air core being formed in the nozzle. The corresponding velocity of atomized liquid at nozzle orifice is the largest. Using a self-designed atomization experiment platform, the velocity and pressure of atomized liquid and the spray cone angle are measured for three nozzles with different orifice shapes. The micro-morphology of Si3N4 particles is also determined. These data confirm the correctness of numerical simulation. Considering atomization performance of the nozzle, the contraction conical nozzle is more suitable for the atomization of Si3N4 in practical production based on the dry granulation approach.

Numerical investigation of two hollow cylindrical droplets vertically impacting on dry flat surface simultaneously

In this paper, the effect of two hollow droplets’ impact on a solid substrate is numerically studied. A coupled level set and volume of fraction method is used to investigate the fluid dynamics and heat transfer characteristics of two hollow cylindrical droplets vertically impacting on a dry flat surface simultaneously. Numerical results show that, different from two continuous dense droplets, counter-jet at impact point (CJIP) is observed as a distinguished feature during the two hollow droplets’ impact process. However, counter-jet at symmetric point (CJSP) is formed in the vicinity of the symmetric point for both two hollow and dense cylindrical droplets. The analysis of pressure and velocity distribution is performed. It is shown that the formation of CJSP and CJIP is mainly caused by the pressure gradient. Upon further analysis of average heat flux, the formation of CJIP and the liquid shell rupture are the two main factors determining that the hollow droplet has a lower heat transfer capacity with the flat solid wall than that of the dense droplet. Through the investigation about the effect of impact velocity on fluid flow and heat transfer characteristics, the spread factor, the height of CJSP and CJIP, and the average heat flux will all increase with higher impact velocity. These results will provide a better understanding of hollow droplet impingement and heat transfer on flat surfaces.

Prediction and CFD Simulation of the Flow over a Curved Crump Weir Under Different Longitudinal Slopes

The benefit of using a weir is that it allows flowrates to be measured and controlled in open channels and streams. The objectives of this research are: (1) to specify a suitable crest depth position as a control section for estimating the flowrate above a curved crump weir at ten different longitudinal slopes and (2) to compare the proposed flowrate versus measured and computational fluid dynamics (CFD)-simulated flowrates. In this research, the crest point of the curved crump weir was considered to be a control section, relating to the critical depth as a function of the crest depth. Experiments with eight different laboratory flowrates of flume were proposed at ten different channel slopes ranging from 0.0 to 2.5%. Statistical analysis of linear regression indicated that the relationship between critical depth and crest depth is 0.913 on average. Based on this finding, a new equation was derived to predict the discharge over the crump weir, which indicated an excellent match compared to the practical and CFD-simulated results (a maximum differences of 4% based on several standard error indexes and a one-way ANOVA). The CFD technique was performed to simulate the velocity and flow pattern of the curve crump weir based on the volume of fraction method. Six selective sections were tested along the flume with a total length of 1.36 m for a case study of 0.912 m3/h flowrate and zero bed slope to investigate and describe the water surface profile. The statistical analysis indicated insignificant differences between the measured and simulated water surface profiles, with a maximum difference of less than 15% observed at the section located at 0.69 m, while the average difference was 4.86% for all sections.

Numerical analysis on the disintegration of gas-liquid interface in two-phase shear-layer flows

The gas-liquid two-phase interfacial flow widely occurs in atomization or liquid film cooling in the field of aerospace engineering. In this paper, the gas-liquid two-phase shear layer is simulated using volume of fraction method by numerical solver Gerris. Both the two-phase interface morphology and growth of the shear layer show a good agreement with previous experimental observation. The disintegration mechanism of the gas-liquid interface is revealed from the simulation results, which is mainly due to the initial perturbation developing in the gas stream. Different disintegration patterns are discovered, which are wavy disintegration, roller type disintegration and breakdown of ligaments under different velocity ratios and density ratios. The shear layer thickness grows faster under higher pressure conditions, which indicates that the interface disintegration is more violent under higher pressure conditions. Increasing the density ratio will lead to higher frequency of the fundamental wave, which determines the first deformation and further breaking-down of gas-liquid interface close to the entrance of the flow.

Simulation results of influence of constricted arc column on anode deformation and melting pool swirl in vacuum arcs with AMF contacts

In the process of vacuum arc breaking, the energy injected into the anode will cause anode melting, evaporation, and deformation, resulting in the formation of the anode melting pool. The anode activities have great influence on the arc behavior. When the arc current is large enough, even the influence of axial magnetic field is considered, the arc column still is in contraction state, which means the arc burns only on a part of the electrode. In this paper, the model of anode melting pool deformation and rotation is used, and the model includes anode melting and solidification module, magneto-hydro-dynamic module of the anode melting pool, the volume of fraction method, and the current continuity equation. In this paper, the diffuse arc area is selected as 100%, 75%, and 50%, respectively. The anode temperature and deformation, the anode melting layer thickness, and the rotational velocity of the anode melting pool are obtained. The results show that when the current is at 17.5 kA (rms) and the diffuse arc area is 100%, the anode's maximum temperature is 1477 K and the crater depth is 0.83 mm. But when the diffuse arc areas are 75% and 50%, the anode's maximum temperatures reach 1500 K and 1761 K, and the crater depths reach 1.2 mm and 3 mm, respectively. Arc contraction will lead to more serious anode deformation. A similar result is obtained when the simulation current is 12.5 kA. Under the similar situation, the simulation results in the crater depth, the residual melt layer thickness, the rotational speed of the melting pool, and the maximum temperature of the anode at current zero are in good agreement with the experimental results.

Optimizing gate location to reduce metal wastage: Co–Cr–W alloy filling simulation

This research aimed at reveal the reasons for the extra Co–Cr–W alloy wastage in the risers in sand casting. The alloy filling behaviour in both the original and modified moulds was investigated numerically. The alloy–air interface was captured by using volume of fraction method. For the original mould, an unfilled volume in the vicinity of the runner bar top was apparent and it was refilled by a back flow, originated from the risers in the late stage of filling. The back flow behaviour required a higher level of the liquid alloy in the risers, which resulted in excessive wastage, and it was essential to form the required shape of the cast. For the modified mould, the unfilled volume was eliminated and the cast part shaping time was reduced to around 10s from 90s. The alloy wastage in the risers was reduced by 11%.

Comparative Study on the AC Brekadown Voltage of Palm Fatty Acid Ester Insulation Oils Mixed With Iron Oxide Nanoparticles

Mineral oils are are derived from petroleum which is a non-renewable and non-sustainable source, and therefore there is a critical need to develop alternative insulation oils for use in transformers. Ester oils offer a number of benefits over mineral oils such as good biodegradability, high cooling stability, good oxidation stability and excellent insulation performance. Nowadays, nanotechnology has become one of the most important research fields in both the academia and industry and it has been shown in previous studies that nanoscale materials are beneficial for transformers. In this regard, the objective of this study is to compare the AC breakdown voltage of palm fatty acid ester (PFAE) oils mixed with iron oxide (Fe<sub>3</sub>O<sub>4</sub>) nanoparticles. The PFAE-based nanofluids are prepared using two methods: (1) Method I (weight-based method whereby the concentration of the Fe<sub>3</sub>O<sub>4 </sub>nanoparticles is 0.01 g/l) and (2) Method II (volume-fraction method whereby the concentration of the Fe<sub>3</sub>O<sub>4 </sub>nanoparticles is 0.01, 0.02 and 0.03%). The AC breakdown voltage test is conducted on the PFAE-based nanofluids in accordance with the ASTM D1816 standard test method. Weibull statistical analysis is carried out to analyse the AC breakdown voltage of fresh PFAE oil and PFAE-based nanofluids. It is found that there is enhancement of the AC breakdown voltage for all PFAE-based nanofluids with the exception of with the exception of one sample prepared using Method II (0.01% Fe<sub>3</sub>O<sub>4 </sub>nanoparticles).

Numerical Study of Transient Deformation and Drag Characteristics of a Decelerating Droplet

A numerical study of the transient deformation and drag properties of impulsively started decelerating drops in axisymmetric flows is conducted. The incompressible Navier–Stokes equations coupled with the volume of fraction method are solved. The differences in the deformation and drag characteristics between the accelerating and decelerating drops are elucidated. The Weber number has a significant influence on the drag properties of the round drops; however, the effect of the Ohnesorge number is small. A dynamic droplet drag model is provided based on the computational fluid dynamics results to predict the drag coefficient of a decelerating drop. In addition, the flow of liquid drops past an RAE2822 airfoil is considered, and its drag is evaluated using the drag model.

CFD Simulation for the Resistance Performance of 1000 Dwt Deep-Vee Vessels on Bulbous Bow

Resistance influence factors of bulbous bow are analyzed with three 1000dwt displacement types Deep-vee forms provided. The free surface viscous flow of these forms is calculated by air-water two phases RANS equations with RNG turbulence model and volume of fraction method. Total resistance, pressure distribution and wave profile of hull are presented. Some results can be taken as follows: Adopted longer protruding length can improve the resistance character at medium high speed and ameliorate the resistance performance in calm water at low speed to design a 1000dwt deep-vee vessel; the bulbous bow wavemaking is only one of the reasons to influence the wavemaking resistance of hull. The importance influence factor of hull wavemaking resistance is how to form advantage disturbance or least disadvantage disturbance between the bulbous bow wave and hull wave.

CFD Simulation for Displacement Deep-Vee Vessels on Resistance Influence Factor

Resistance influence factors of displacement type Deep-vee forms are analyzed with eight hull forms provided. The free surface viscous flow of these forms is calculated by air-water two phases RANS equations with RNG turbulence model and volume of fraction method. Total resistance, pressure distribution and wave profile of bow are presented. Some results can be taken as follows: while maintaining the same tonnage, L/B ratio and draft, the resistance performance of Deep-Vee vessels is excellent at high speed if a large transverse dead rise angle was located from 50%front midship to 25% backward midship; The resistance performance at a lesser L/B and draft is worse if the displacement and dead rise angle is the same; Furthermore, it can be improved by a cigar-shaped bulbous bow. The change of pressure distribution for cigar-shaped bulbous bow is more slightly than that of tobacco pipe-shaped bulbous bow.

Investigation of Two-Phase Transport in Polymer Electrolyte Fuel Cell Channels Using the Volume of Fraction Method

Two-phase flow in the gas channel of a polymer electrolyte fuel cell (PEFC, also called PEM fuel cells) is investigated using the volume of fraction (VOF) method. We examine two-phase flow patterns, pressure drop and water droplet formation at various hydrophobic surfaces. Evolution of pressure drop is also presented to indicate its dependence on the two-phase transport status. The results also show that in the regime of high water flow rate and low gas velocity the slug annular flow emerges. When the gas flow increases, the annular type flow occurs. Experimental test is also conducted to compare with the numerical result. The developed numerical tool can be employed to investigate the fundamentals of channel two-phase flow in fuel cell.

Microstructure Characterization and Modeling of Splat Formation during Air Plasma Spraying for Inconel 625 Superalloy

There is a growing interest in use of the nickel-based alloy Inconel 625 coatings due to its ability to improve base materials high temperature properties. Thermal spraying methods such as Air Plasma Spraying (APS) can be considered as a convenient method to deposit this material. The present work deals with APS deposited Inconel 625 structures consisting of huge number of individual splats formed by impacting molten droplets on substrates during spraying process. It is clear that the splat formation mechanism which dominates its size, cohesion, and boundaries highly influences the microstructure of the coating. This paper presents a developed numerical technique performed to simulate splat formation using a three dimensional model. In this method flow field is solved by Finite Volume Method (FVM) and free surfaces are determined from Youngs’ Volume of Fraction method (VOF). Finally, the model prediction is correlated with the actual splat geometries.

An “Attachment Kinetics-based” Level-set Method for Macromolecular Crystallization under Buoyancy-driven Convective Effects

A level-set method, specifically conceived for the case of organic crystal growth from supersaturated solutions, is introduced and described in detail. The model can simulate the growth due to the slow addition of solute molecules to the surface of a lattice and can handle the shape of macromolecular growing crystals under the influence of natural convection. It is carefully developed according to the complex properties and mechanisms of protein crystal growth taking into account the possibility of anisotropic growth due to either “faceted” surface-orientation-dependent behaviors or the influence of external convection occurring in the protein reactor. The analogies and differences between this technique and a previous volume of fraction method are discussed in terms of theoretical aspects and fundamental equations. The advantages and limitations of both formulations are pointed out.

Growth and mutual interference of protein seeds under reduced gravity conditions

This analysis deals with new models and computational methods as well as with novel results on the relative importance of “controlling forces” in macromolecular crystal growth. The attention is focused in particular on microgravity fluid-dynamic aspects and on the case of the simultaneous growth of different seeds. A “kinetic-coefficient-based” volume of fraction method is specifically and carefully developed according to the complex properties and mechanisms of macromolecular protein crystal growth. It is shown that the size and the shape of the growing crystals play a “critical role” in the relative importance of surface effects and in determining the intensity of convection. Convective effects, in turn, are found to impact growth rates, macroscopic structures of precipitates, particle size and morphology as well as the mechanisms driving growth. The face growth rates in particular depend on the complex multicellular structure of the convective field and on associated “pluming phenomena.” The relative importance of mass transport in liquid phase and surface attachment kinetics is investigated. The simulations show that it does not behave as a “fixed” parameter and that different crystallization conditions may occur in the protein chamber due to mutual interference of the growing seeds, complex convective effects and the “finite size” of the reactor.